A, B, and C try to hit a target simultaneously but independently. Their respective probabilities of hitting the target are\({3\over4},{1\over2},{5\over 8}\). The probability that the target is hit by A or B but not by C is

A bag contains 5 white and 3 black balls. Five balls are drawn successively without replacement. The probability that they are alternately of different colours is

If two events A and B are independent such that P(A) = 0.35 and \(P(A\cup B)=0.6\), then P(B) is

If m is a number such that m \(\le\) 5, then the probability that quadratic equation 2x² + 2mx + m + 1 = 0 has real roots is

A speaks truth in 75% cases and B speaks truth in 80% cases. Probability that they contradict each other in a statement is

A box contains 10 good articles and 6 with defects. One item is drawn at random. The probability that it is either good or has a defect is

If A and B are two events such that P(A) = \(\frac { 4 }{ 5 } \) and \(P(A\cap B)=\frac { 7 }{ 10 } \) then P(B/A) = 

If P(A)=\(\frac { 1 }{ 2 } \), P(B)=\(\frac { 1 }{ 3 } \) and P(A/B) = \(\frac { 1 }{ 4 } \), then \(P(\bar { A } \cap \bar { B } )\) =

If P(A) = 0.4, P(B) = 0.3 and P(AUB) = 0.5, then \(P(\bar { B } \cap A)\)

A flash light has 8 batteries out of which 3 are dead. If 2 batteries are selected without replacement and tested, the probability that both are dead is

If an experiment has exactly the three possible mutually exclusive outcomes A, B, and C, check in each case whether the assignment of probability is permissible.
\(P(A)=\frac { 1 }{ \sqrt { 3 } } ,\quad P(B)-1-\frac { 1 }{ \sqrt { 3 } } ,\quad P(C)-0\)

An experiment has the four possible mutually exclusive and exhaustive outcomes A, B, C, and D. Check whether the following assignments of probability are permissible.
P(A) = 0.22 , P(B) = 0.38 , P(C) = 0. 16, P (D) = 0.34

If \(P(A)=0.6, P(B)=0.5\) and \(P(A \cap B)=0.2\) Find \(P(A / \bar{B})\)

The probability that student selected at random from a class will pass in Mathematics is \(\frac { 2 }{ 3 } \) and the probability that he passes in Mathematics and English is \(\frac { 1 }{ 3 } \). What is the probability that he will pass in English if it is known that he has passed in Mathematics?

Given that the events A and B are such that P(A) = \(\frac { 1 }{ 2 } \), P(AUB) = \(\frac { 3 }{ 5 } \) and P(B) = p. find P if they are mutually exclusive events. 

A problem in Mathematics is given to three students whose chances of solving  \(\frac { 1 }{ 3 } ,\frac { 1 }{ 4 } \) and \(\frac { 1 }{ 5 } \) (i) What is the probability that the problem is solved? (ii) What is the probability that exactly one of them will solve it?

A firm manufactures PVC pipes in three plants viz, X, Y, and Z. The daily production volumes from the three firms X, Y and Z are respectively 2000 units, 3000 units, and 5000 units. It is known from the past experience that 3% of the output from plant X, 4% from plant Y and 2% from plant Z are defective. A pipe is selected at random from a day’s total production,
(i) find the probability that the selected pipe is a defective one.
(ii) if the selected pipe is a defective, then what is the probability that it was produced by plant Y?

The probability of an event A occurring is 0.5 and B occurring is 0.3. If A and B are mutually exclusive events, then find the probability of
(i) \(P(A\cup B)\) (ii) \(P(A\cap \bar { B } )\) (iii) \(P(\bar { A } \cap B)\)

One card is drawn from a well shuffled pack of 52 cards. If E is the event, "the card drawn is a king or queen" and F is the event "the card drawn is a queen or an ace", then find P(E/F).

A bag contains 10 white and 15 black balls. 2 balls are drawn in succession without replacement. What is the probability that first is white and second is black?

If A and B are two independent events such that P(A\(\cup \)B) = 0.6, P(A) = 0.2,  find P(B).

Two cards are drawn from a pack of 52 cards in succession. Find the probability that both are Jack when the first drawn card is (i) replaced (ii) not replaced.

Urn-I contains 8 red and 4 blue balls and urn-II contains 5 red and 10 blue balls. One urn is chosen at random and two balls are drawn from it. Find the probability that both balls are red.